In daily life or scientific and technological research, we often need to speed up the slow changing process, so that we can quickly understand all the process in general, or we need to slow down the fast changing process, so that we can find out any specific changes in detail in the changing process, which is called time stretch. Based on the application of the time stretch, there is a fast sampling technique based on a narrow pulse control signal which is usually used to rapid physical field of research, such as blasting, nuclear electronics, elementary particle movement characteristics, as well as a photoelectric signal sampling oscilloscope. However, the sampling technique is restricted by the sampling time which may become the limits of its temporal resolution. Thus, some details in the time that is smaller than the sampling time can not be distinguished, and the details will be attenuated and annihilated after sampling processing. In addition of the information sampling technique, the time measurement technology used for the time interval measurement is also used for time stretch to achieve higher temporal resolution. The commonly used method includes: converting the time quantum to other physical quantities according to the characteristic of the measured signal, or indirectly enlarging measured signal based on the asymmetry of the signal establishment and release. However, the former is limited by response time of the conversion devices and is not directly used to the original signal, while the latter can not further parse multiple objects and more details.
In order to further illustrate the problems of the time stretch technology, several common techniques are analyzed as following.
The sampling technique is an important means to study the fast physical, which commonly includes a high-speed photography and optical sampling oscilloscope. The former is mainly used to take a picture for the fast moving object, which has a relatively long sampling interval, where the picture is commonly flat image information (referring to: Li, Jing-Zhen, , Science in China Series E: Technological Sciences, 2009, 39(12): 1887-1904 ISSN: 1006-9275). The latter is mainly used for signal testing in optoelectronics engineering, which has a relatively short sampling interval (usually approximates a continuous signal) and includes a single or multiple channels (referring to: Zhou Xuan, Li Jin-Lin and Bao Bing-Qian,  Electronic Measurement Technology, Issued 02, 1984, ISSN: 1002-7300.0.1984-02-000).
Both of these applications must use the narrow pulse signal with a short period, which is also the limit of the temporal resolution of the measured signals. Even if the fast-changing physical process can be slowly displayed to achieve the purpose of understanding the details of the changing process, the two applications need the sampling signal or response time with the shorter period than the observed objects, thus limiting our observation for the high-speed changing objects. Even if the period of the observed objects is consistent with that of the sampling signal or response time, we can not get the details of the observed objects. Thus, the time stretch technology based on the sampling technique is not (partially) stretch the time actually, which is need rely on the narrow pulse signal with a shorter period, while the change rate of the observed objects to the observer/receiver remains unchanged. In addition, the technology is irreversible and can only be used to obtain detailed contents rather than compressed information.
Time conversion technique is usually used to the time-to-digital converter (TDC), the vernier timer, the time-to-amplitude converter (TAC), the delay line coding technique and the interpolation technique, which is based on pulse time interval measurement.
(1) The interpolation technique is based on the sum and difference of the inherent delay time of the device and the time interval of the signal to increase the time interval of the signal, and the logical operations and capacitor charging/discharging is operated to achieving the delayed amplification of the signal and finally realize the effect of expanding the time interval. The interpolation technique can also be called as time interval replication technology, and the proportional amplification of the pulse interval is still achieved by using the asymmetry of the signal paths. This technology can not directly amplify the time interval of the original signals, which is achieved after a number of middle conversions. Except for the measurement of a single time interval signal, the interpolation technique can not be used for other occasions.
(2) The delay line coding technique can be achieved based on the states when the inherent time difference of the signal transmission circuit reaches the gate circuit and when a synchronous clock locking signal reaches each gate circuit. This technology is only designed to reduce the frequency of the count clock, the time interval of the measured signal is not expanded, and the resolution of the time interval is improved only depending on the shorter response time of the circuits.
(3) TAC technique is an indirect measurement method that uses the characteristics of the signal amplitude changing with time and estimate the time interval by measuring the amplitude and/or phase, which is also the basis of time-digital converter. However, because the TAC technique does not directly measure the time interval, this technique depends on the continuous and stable change of the signal amplitude of the foregoing components and the strict correlation between the time interval and the amplitude.
(4) TDC, such as Wilkinson-type TDC, is achieved by time-to-amplitude conversion and then by amplitude-to-digital conversion. In addition to the comprehensive application of the aforementioned methods, the asymmetry for signal establishment and release may be used as the starting of the time stretch processing, which can proportionally amplify the time interval. However, this method still can not amplify the time interval directly, but achieve the amplified time interval indirectly according to the electrical characteristics of the accumulation and release process of the charges on the capacitor. Thus, there is a strict demand of the capacitor and the charging/discharging circuits, and a poor anti-interference. This time interval amplification technology usually exists time dead-zone, and can not effectively process multiple target signals (more than one time interval signal) and the continuous changing analog signal.
Some devices similar to the TDC, such as, digital video, film, voice decoder are also usually used for the time stretch technology. However, on the one hand, the information is a record of the original signal, rather than represents the actual contents of the original signal. On a more basic level, when the information is saved, the original signal is used as control variable to influence the state of other substances, and the characteristics of the original signal is responded by the state of other substances. On the other hand, the method for receiving/transmitting digital coding at different rates is usually used, and the detail portion of the signal after the digital coding (sampling techniques) has been lost (limited by the sampling pulse frequency). Therefore, they can not reflect the actual results of the time stretch processing of the original signal.
In summary, the foregoing time stretch technologies can not achieve a good compatibility on direct processing, nonrestraint of response time, process of analog signal process of multiple time interval objects on the same channel, the reversible transformation and the smaller lossless signal details. In addition, most of the programs do not really change the local time of the observed objected and the observer/receiver.